100 LearnersLast updated on May 26th, 2025
Factors of 868
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 868, how they are used in real life, and tips to learn them quickly.
What are the Factors of 868?
The numbers that divide 868 evenly are known as factors of 868.
A factor of 868 is a number that divides the number without remainder.
The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, and 868.
Negative factors of 868: -1, -2, -4, -7, -14, -28, -31, -62, -124, -217, -434, and -868.
Prime factors of 868: 2, 7, and 31.
Prime factorization of 868: 22 × 7 × 31.
The sum of factors of 868: 1 + 2 + 4 + 7 + 14 + 28 + 31 + 62 + 124 + 217 + 434 + 868 = 1792
How to Find Factors of 868?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 868. Identifying the numbers which are multiplied to get the number 868 is the multiplication method.
Step 1: Multiply 868 by 1, 868 × 1 = 868.
Step 2: Check for other numbers that give 868 after multiplying
2 × 434 = 868
4 × 217 = 868
7 × 124 = 868
14 × 62 = 868
28 × 31 = 868
Therefore, the positive factor pairs of 868 are: (1, 868), (2, 434), (4, 217), (7, 124), (14, 62), (28, 31).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 868 by 1, 868 ÷ 1 = 868.
Step 2: Continue dividing 868 by the numbers until the remainder becomes 0.
868 ÷ 1 = 868
868 ÷ 2 = 434
868 ÷ 4 = 217
868 ÷ 7 = 124
868 ÷ 14 = 62
868 ÷ 28 = 31
Therefore, the factors of 868 are: 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 868 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
868 ÷ 2 = 434
434 ÷ 2 = 217
217 ÷ 7 = 31
31 ÷ 31 = 1
The prime factors of 868 are 2, 7, and 31.
The prime factorization of 868 is: 22 × 7 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 868 is divided by 2 to get 434.
Step 2: Now divide 434 by 2 to get 217.
Step 3: Then divide 217 by 7 to get 31. Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 868 is: 22 × 7 × 31.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 868: (1, 868), (2, 434), (4, 217), (7, 124), (14, 62), (28, 31).
Negative factor pairs of 868: (-1, -868), (-2, -434), (-4, -217), (-7, -124), (-14, -62), (-28, -31).
Common Mistakes and How to Avoid Them in Factors of 868
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 868, 1 and 868 are also factors.
Factors of 868 Examples
Problem 1
A group of 7 friends has 868 chocolates. How many chocolates will each friend get if they divide them equally?
Each friend will get 124 chocolates.
Explanation
To divide the chocolates equally, we need to divide the total chocolates by the number of friends.
868 ÷ 7 = 124
Problem 2
A rectangular garden has a length of 31 meters and a total area of 868 square meters. Find the width.
28 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
868 = 31 × width
To find the value of the width, we need to shift 31 to the left side.
868 ÷ 31 = width
Width = 28.
Problem 3
There are 31 gift bags, and 868 candies. How many candies will be in each bag?
Each bag will have 28 candies.
Explanation
To find the candies in each bag, divide the total candies by the number of bags.
868 ÷ 31 = 28
Problem 4
In a school, there are 868 students and 62 classrooms. How many students are there in each classroom?
There are 14 students in each classroom.
Explanation
Dividing the students by the total number of classrooms, we will get the number of students in each classroom.
868 ÷ 62 = 14
Problem 5
A library has 868 books and 28 shelves. How many books will go on each shelf?
Each shelf will have 31 books.
Explanation
Divide the total number of books by the number of shelves.
868 ÷ 28 = 31
FAQs on Factors of 868
1.What are the factors of 868?
2.Mention the prime factors of 868.
3.Is 868 a multiple of 4?
4.Mention the factor pairs of 868?
5.What is the square of 868?
Important Glossaries for Factor of 868
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, and 868.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 31 are prime factors of 868.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 868 is 22 × 7 × 31.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 868 are (1, 868), (2, 434), etc.
- Negative factors: Factors that are negative numbers. For example, the negative factors of 868 are -1, -2, -4, -7, -14, -28, -31, -62, -124, -217, -434, and -868.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
